How to generalize the Ehrenfest theorem and the uncertainty principle

2019/04/12 by Renziehausen, Klaus, Barth, Ingo
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1904.06177

Abstract

The Ehrenfest theorem and the Robertson uncertainty relation are well-known basic equations in quantum mechanics. However, there exist problematic cases, where the Ehrenfest theorem and the Robertson uncertainty relation are not correct. These cases occur when the azimuthal angle in polar or spherical coordinates is used within these equations. The purpose of this paper is to present and discuss a generalized Ehrenfest theorem and a generalized uncertainty relation which are still valid for these cases. Hereby, we define and use a mathematical operation called expectation commutator.

Related

• Generalized proof of uncertainty relations in terms of commutation relation and interpretation based on action function
• General and Stronger Uncertainty Relation
• Do the Robertson-SCHRÖDINGER and the Heisenberg Uncertainty Relations Imply a General Physical Principle ?
• On the uncertainty relations for angular observables and beyond them
• The generalized uncertainty principle within the ordinary framework of quantum mechanics